Some aspects of the homogeneous formalism in field theory and gauge invariance

Marcella Palese and Ekkehart Winterroth

Department of Mathematics, University of Torino, via C. Alberto 10, 10123 Torino, Italy


We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a {\em formal energy} for a parametrized version of the Hilbert--Einstein Lagrangian and we show that this quantity is conserved.

AMSclassification. 53C05, 58A20, 70H05, 70S05, 83C40.

Keywords. Jets, connections, homogeneous formalism, Hamilton equations, energy, gravity.